The intergalactic medium (IGM) is a key probe of both cosmology and galaxy formation. Most of our knowledge of the IGM, comes from absorption line measurements---1-dimensional skewers along the way toward bright background sources. In the era of hydrodynamic cosmological simulations, this information represents just a small fraction of the full 3-dimensional information encoded in current theoretical models for the properties of the IGM. In the era of large telescopes, it also represents only a fraction of the information that is observationally accessible. It is now possible to make predictions for the Lyman alpha emission from the IGM, that provide spatial and kinematic information about the IGM. I will discuss the theoretical advances that have made this possible and compare to current observations, as well as highlight future possibilities for understanding the distribution of neutral gas at high redshift as well as the physical processes that result in Lyman alpha emission.